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CFD Analysis of Metro Car (COVID-19)May 5th, 2020

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Introduction & Objectives

• Hexagon develops software technologies in the area of Computational Aided Engineering (CAE) used by leading industrial companies in automotive, aerospace, electronics, consumer goods, medical equipment & more

• CAE is used to predict virtually complex physical phenomena and covers all engineering disciplines such as structural analysis, electromagnetics, acoustics, fluid mechanics, among others

• The discipline of simulating fluid phenomena is named Computational Fluid Dynamics (CFD)

• The goal of the present work is to apply CFD technologies to improve the understanding of the effect of some parameters on the propagation of the droplets involved while sneezing, breathing or speaking

• The objective of the authors of this work is to assist the authorities and the public with their understanding, in view of future lockdown exit strategies

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Metro Car

Breathing & Speaking in Confined Spaces

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Generic Metro Car with background Air-Condition airflow

Simulation Scenario, Breathing & Speaking Persons Close to Each Other

Global • A generic metro/train car with persons spread out• Persons are closer to each other than the recommended

social distance of 1.5m ~ 2.0m• One person emits particles and is assumed to be speaking

(red person in car)• The opposing person sits approximately 0.7m away from

the speaking person (emitter)• All other persons are only breathing through the mouth• Simulated physical time is 180 seconds

Cases:• Case #1 emitting person does not wear a mask• Case #2 emitting person wears a mask

0.7m

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General simulation set-up

Software:• The CFD solver used to perform this work is Cradle CFD (scFlow v2020)

from Hexagon• More information and validation examples are available upon request

Droplet physics:• A simple approach called ‘particle tracking’ (diluted droplet into air) is used to

model the droplets which result in:• Take drag force, gravity, etc. in consideration• No evaporation, no break-up/collapse of droplets• No interaction between particles (droplets)

• No consideration on virus behavior, only air-flow and water droplets (particles) movement

• When particles meet objects, they are arrested• Particles were counted on the hands and faces of persons

Turbulence:• The SST k-omega model was used

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CFD Boundary conditions on PersonsApproximation of Breathing Cycles

Breathing cycles:• Person Breathing boundary condition according to the graph to the top right

• Breathing rate (c-rate) of 5 sec [1]• Flow pattern approximated by figure 1 presented by Gupta et. al. [2]• Flow rate of 600ml/stroke for European individual derived by 1.2 times 500ml/stroke for Japanese

individual [1]

• Person Speaking boundary condition according to the graph to the bottom right• Maximum exhalation rate of 5.e-4 m3/s [2] (figure 9c in reference)• Breathing rate depend on language. Same breathing rate as for breathing was assumed• To approximate longer exhales during speaking exhaling was extended to 3.5s and inhale to 1.5s• Air flux rate per stroke was balances so inhale and exhale is same volume

• Both the speaking and breathing case resulting flow velocity of 0.5m/s and 0.34m/s is in accordance with data summarized by Zhang et. al. [3]

• Breathing References:[1] Breathing reference numbers and formulas, Kyoto Prefectural University of Medicine, viewed 30 April

2020 , <http://www.f.kpu-m.ac.jp/k/picu/respiration/res-c-2.html> (Japanese)access reference here

[2] Gupta J. K. et. al., 2010, “Characterizing Exhaled Airflow from Breathing and Talking”, Indoor Air, 20, pp. 31-39access reference here

[3] Zhang H. et. al., 2015, “Documentary Research of Human Respiratory Droplet Characteristics”, Procedia Engineering, vol. 121, pp.1365-1374access reference here

-0.0004-0.0003-0.0002-0.0001

00.00010.00020.00030.0004

0 1 2 3 4 5 6

Table for Breathing (m3/s - sec)

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0 1 2 3 4 5 6

Table for Speaking (m3/s - sec)

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CFD Boundary conditions on EmitterApproximation of Droplet Generation

Droplet Generation when Speaking:• This boundary condition only apply to the speaker

• Droplets is modelled as particles that are interacting with surrounding air

• Droplet Distribution:• Droplet (”particle”) diameter distribution were approximated by a Nukiyama-Tanasawa distribution to

approximate distribution found in figure 7a presented by Xie et. al. [1]• Droplet mean diameter of 40 micrometer, density same as water and 1000 droplets were generated per breathing

stroke with a mass of 3.35e-8 kg• Note that the large droplets were under-estimated by the distribution, but as they are heavy they will fall down

quicker so the distribution were tuned to agreeing with smaller sized droplets according to [1].

• Droplet splay during speaking:• Droplet spay were estimated by results presented by Gupta et. al. [2], see figure 6 in reference.• A fan shaped spray with spread angles of 5degree and length of 0.03m (long axis) and

15degree and length 0.015 m (short axis)

• Droplet References:[1] Xie, X. et. al., 2009, “Exhaled droplets due to talking and coughing”, J. R. Soc. Interface 6, pp. 703-714

access reference here[2] Gupta J. K. et. al., 2010, “Characterizing Exhaled Airflow from Breathing and Talking”, Indoor Air, 20, pp. 31-39

access reference here

-0.000001

0

0.000001

0.000002

0.000003

0.000004

1 10 100 1000

Input distrubition in scFLOWNukiyama Tanaswa with

40micron, a= 10, b=1

Splay modelTop view Side view

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CFD representation of mask as porous mediaApproximation of mask

Mask:• Pressure drop is considered without any deformation of the mask (porous media)

• Pressure drop has been calibrated from a well-known surge mask producer• Shape was approximated by surgical mask

• A simple filtering effect of particle was considered (see next page)

Porous media:• Mask pressure drop is modeled as porous media using following equation:

Mask used in Case #2

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CFD Boundary condition of Mask/throat volumeApproximation of Mask filtration effect

Mask Filtering• A simple approach is used: when a droplet was generated (as most droplets

reach mask volume) additional arresting force is added to it• For each particle, a random number between 0 and 1 was generated.• When the particle reach the mask volume this number is compared to the mask efficiency

• If the random number is greater than the efficiency the particle is let though the mask• If the random number is less than the efficiency the particle is arrested

• As most particles reached the volume where the check takes place the check was done when the particles was created instead in order to speed-up the simulation as the number of droplets could be reduced.

• Filtration efficiency presented by Sanchez in figure 32 [1] was used to arrest the particles.

• Filtration Reference:[1] Sanchez E., “Filtration Efficiency of Surgical Masks”, MSc theses, University

of South Florida, Tampaaccess reference here

Simple test, mainly smallest droplet can pass through the mask

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Based on Japan Rain CarsApproximation of Metro car Air-Conditioning System

Air-Conditioning system in wagon• Flow rate into the car was estimated to 19 m3/min

• Based on Mitsubishi Eclectic air-condition system for JR East E233 series cars [1]

• To keep the ventilation efficiency same as in the reference the flow rate is scaled with the fraction of volumes between the two metro car types

• The air supply and return air exits was estimated as shown in the picture to the right.• Estimation was based on reference pictures from the inside of the

JR East E233 cars [2]

• Car Air-conditioning Reference:[1] Koga T., 2018, “Features and Maintainability Improvement of

Railcar Air Conditioning Unit for JR EAST E235 Series”, MITSUBISHI DENKI GIHO, vol.92, no.7 pp.26-29 (Japanese)access reference here

[2] JR East E233 series 1000 series, Fukuju Train Net, viewed 2 May 2020 , <https://ftnp6.web.fc2.com/trainseat/jreast/E233-1000.html> (Japanese)access reference here

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Overall View of Simulations

Metro Car with Speaking & Breathing Persons (case #1 & #2)

Remark: Physical time is 180 sec

The emitted particles come from the mouth of a person that is assumed to be speaking

The sitting person is 0.7m away from the opposing speaking person (emitter)

All persons are assumed to be breathing from the mouth.

A very simple air-conditioning system were considered

Under the conditions assumed in the simulations a mask can reduce the droplets that reach the opposing person from the emitter

Watch Video: https://www.youtube.com/watch?v=kdfFUg_m-pA

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Droplet count on Face & Hands after 180 secondsSpread of Aerosol Droplets due to Speaking

Note that this is a simulation aiming to replicate physical behavior of air-born droplets under realistic conditions.It is not a medical advice.

The close distance between the person shows the importance of social distancing. Please follow the guidance from your local authorities.

Under the assumption presented a surgical mask have the potential to reduce air-born droplet that are spread to the environment.

In this specific case it was found that the droplets reaching the opposing person was greatly reduced when the emitter had a simple surgical mask.